Electromagnetic Induction, 347 



average electromotive force e which acts in the secondary 

 circuit during the movement is 



M 2 -M l n 



and if r be the resistance of the secondary circuit, the average 

 strength of the secondary current is 



e==e= M 2 -M l a 

 r rt 



The total quantity, q, of electricity conveyed by the secondary 

 current is consequently 



q — ct-=. — (J, 



and is therefore independent of the time occupied in the 

 displacement of the secondary coil. 



The values of M l and M 2 , the coefficients of induction 

 corresponding to the initial and final positions of the secondary 

 coil, can be obtained by inspection of diagrams of curves of 

 constant induction such as those which accompany this paper. 

 It is evident that the total secondary current is nothing in 

 every case in which the secondary coil is moved so as to 

 make M 2 = M X (that is, whenever the secondary coil in its 

 final position is on the same curve as in its first position), and 

 that the secondary current is positive when the absolute value 

 of M 2 is greater than that of M 1; and negative when M 2 is less 

 than Mi. 



The spaces between the curves in the figures may be filled 

 up as follows by other curves, for which the values of M lie 

 within the available range of the curve fig. 1. Assume a 

 value for M which will lie between its values for two curves 

 already drawn ; take this as the value of z, and find the point 

 of the curve fig. 1 to which it corresponds. A point on the 

 axis of x will thus be found, which will divide the distance 

 between the two points on that axis, whose values are those 

 of x for the given curves, into two parts whose ratio may 

 easily be found. Then, if a series of points between the two 

 given curves are found for which this ratio is constant, a 

 curve joining these points will be a curve of constant induction, 

 for which the value of M will be that which was assumed. 



The curves of constant induction may also be employed in 

 a graphic method for determining, at a number of points in 

 the magnetic field, the direction of the resultant inductive 

 effect on the secondary coil in the positions in which it was 

 used in the measurements for determining the two sets of 



